Short answer: Any modern considered-secure symmetric cipher is fine. Just use AES with a secure mode of operation, like CBC or GCM.
Known plaintext attacks are a standard part of cryptanalysis; any cipher that is even marginally weaker against them than otherwise is considered cryptographically compromised.
Longer answer: This is an excellent risk to consider, but you're kind of asking the wrong question. Leaving aside the why (that is, why are you trying to roll your own data encryption scheme, when so many already exist?), you should probably consider where the assumption that
this makes finding the key with brute force easier
comes from. Even if you HMAC the data with a different key (not possible if using an authenticated encryption scheme like AES-GCM), if you have any way to determine a correct key from an incorrect one (such as a hash of the key, or of the plaintext, or even just because you make the assumption that if it decrypts into syntactically-valid JSON the key is probably right), an attacker can do the same thing. Being able to near-instantly validate the correctness of the correct key is just assumed to always be the case.
The difficulty of brute-forcing modern crypto isn't because you don't have a partial plaintext in systems that use it, or because it's hard to know when you've guessed the right key. It's because the key space is so large that, if you built an entire datacenter full of top-of-the-line hardware that did nothing but try a distributed attack to brute-force a single 128-bit AES key and could run forever, the machines in that datacenter would be absurdly unlikely to guess the right key before the sun expanded to swallow the earth.
That's not hyperbole, by the way; human intuition is just really bad at big numbers, and 2^128 is an extremely big number. Let's say you put a million (OK, 2^20) CPUs in the hardware in that datacenter. Let's further assume that each of them can check 32 billion (2^35) possible keys per second (which is faster than even the best hardware-accelerated modern commodity CPUs I'm aware of, but you've got some fancy custom hardware). That means your whole datacenter can check 2^55 (about 32 quadrillion) possible keys per second. Super fast, right? At that rate, and assuming that on average you only have to search half of the keyspace, you will need (2^127)/(2^45) = 2^82 seconds to have a 50% chance of finding the key.
The sun is expected to swallow the earth in roughly 7.6 billion years (give or take a few thousand millennia). In seconds, that's 2.4x10^17, also written as 2.4e17. Take the base 2 logarithm of that number, and you get a bit less than 58. 2^82 / 2^58 is 2^24, or about 16 million. You would be roughly one six-millionth of a percent of the way done.
Also, not part of your question, but: you are taking into account integrity (detecting tampering with the ciphertext, which most encryption provides little if any protection against) and also generating unique initialization vectors for your files, right? Doing crypto right is hard. There's already (tons of) programs out there that do symmetric encryption of files (or other data blobs).